Use graph paper for this question. Take 1 cm = 1 unit on both the axes.

(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Construct the point P such that PA = PB and P is equidistant from AB and AC.

Steps of construction :

1. Plot the points A(1, 1), B(5, 3) and C(2, 7).

2. Draw WZ, the perpendicular bisector of AB.

3. Draw PS, the angle bisector of ∠CAB.

4. Mark point P, the intersection of WZ and RS.

(ii) We know that,

Locus of point equidistant from two points is the perpendicular bisector of the line joining the two points.

Hence, locus of points equidistant from A and B is WZ.

(iii) We know that,

Locus of point equidistant from two sides is the angle bisector of the angle between two sides.

Hence, locus of points equidistant from AB and AC is PS.